A universally composable (UC) blind signature functionality requres users to commit to the message to be blindly signed. It is thereby impossible to realize in the plain model. This paper shows that even non-committing variants of UC blind signature functionality can not be realized in the plain model. We characterize UC non-committing blind signatures in the common reference string model by presenting equivalent stand-alone security notions under static corruption. Usefulness of the characterization is demonstrated by showing that Fischlin’s basic stand-alone blind signature scheme can be transformed into a UC non-committing blind signature protocol without using extra cryptographic components. We extend the results to the adaptive corruption model and present analogous notions, theorems, and constructions both in the erasure model and the non-erasure model.